{
  "id": "2401.08802",
  "version": "v1",
  "published": "2024-01-16T19:46:49.000Z",
  "updated": "2024-01-16T19:46:49.000Z",
  "title": "Rates of convergence in CLT and ASIP for sequences of expanding maps",
  "authors": [
    "Dmitry Dolgopyat",
    "Yeor Hafouta"
  ],
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We prove Berry-Esseen theorems and the almost sure invariance principle with rates for partial sums of the form $S_n=\\sum_{j=0}^{n-1}f_j\\circ T_{j-1}\\circ\\cdots\\circ T_1\\circ T_0$ where $f_j$ are functions with uniformly bounded ``variation\" and $T_j$ is a sequence of expanding maps. Using symbolic representations similar result follow for maps $T_j$ in a small $C^1$ neighborhood of an Axiom A map and H\\\"older continuous functions $f_j$. All of our results are already new for a single map $T_j=T$ and a sequence of different functions $(f_j)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-16T19:46:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "expanding maps",
      "symbolic representations similar result",
      "convergence",
      "sure invariance principle",
      "single map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}